Problem: What do the following two equations represent? $2x-3y = -3$ $-6x+9y = 9$
Solution: Putting the first equation in $y = mx + b$ form gives: $2x-3y = -3$ $-3y = -2x-3$ $y = \dfrac{2}{3}x + 1$ Putting the second equation in $y = mx + b$ form gives: $-6x+9y = 9$ $9y = 6x+9$ $y = \dfrac{2}{3}x + 1$ The above equations turn into the same equation, so they represent equal lines.